Question

If one of the legs of a right triangle is 4 in and the hypotenuse is 8 in, find the length of the other leg (use a calculator if necessary). Can you guess the measures of the acute angles?

The answer should be formatted like this:

The length of the other leg is __ in
The measures of the acute angles are : __ and __

Answer 1

The length of the other leg is 6.9 inches.The measure of each acute angle is 45 degrees.

Answer 2

General Idea:

By using the Pythagorean theorem which states that in a right triangle the sum of square of two legs is equal to the square of hypotenuse. We can find the length of the third side.

Given:

`a= 4 \; in\\\\c=8\; in\\\\a^2+b^2=c^2\\\\4^2+b^2=8^2\\16+b^2=64\\Subtracting \; 16 \; on \; both \; sides\\\\b^2=64-16\\b^2=48\\Take \; square \; root \; on \; both \; sides\\\\b= √(48) = √(16 * 3) = √(16) * √(3) = 4 √(3) inches`

We can see shortest side a is 4 inches, hypotenuse is c is 8 inches and middle side is 4√3. This is quality of a special triangle. The smallest side (a) is opposite the smallest angle (30°), the middle side (b) is opposite the angle (60°) and the longest side (c) is opposite the largest angle (90°).

The triangle 30°-60° - 90° triangle will be of the ratio 1:√3:2.

Conclusion:

The length of the other leg is 4√3 in

The measures of the acute angles are : 30° and 60°